xin jin - wur...iii drying of healthy foods from mechanism to optimization xin jin thesis submitted...

Drying of Healthy Foods

From Mechanism to Optimization

Xin Jin

ii

Thesis committee

Promotors

Prof. Dr. G. van Straten

Professor of Systems and Control

Prof. Dr. R.M. Boom

Professor of Food Process Engineering

Co-promotors

Dr. A.J.B. van Boxtel

Associate professor, Biomass Refinery and Process Dynamics Group

Dr. R.G.M. van der Sman

Assistant professor, Food & Biobased Research

Other members

Prof. Dr. M.A.J.S. van Boekel, Wageningen University

Prof. Dr. J.P.M. van Duynhoven, Wageningen University

Dr. M.A. Boon, Dutch Institute for Applied Science (TNO), Zeist, The Netherlands

Dr. K.C. van Dyke, Danone, Wageningen, The Netherlands

This research was conducted under the auspices of the Graduate School VLAG (Advanced

studies in Food Technology, Agrobiotechnology, Nutrition and Health Sciences).

iii

Drying of Healthy Foods

From Mechanism to Optimization

Xin Jin

Thesis

submitted in fulfillment of the requirements for the degree of doctor

at Wageningen University

by the authority of the Rector Magnificus

Prof. Dr M.J. Kropff,

in the presence of the

Thesis Committee appointed by the Academic Board

to be defended in public

on Wednesday 30 October 2013

at 4 p.m. in the Aula.

iv

Xin Jin

Drying of Healthy Foods: From Mechanism to Optimization, 168 pages

PhD thesis, Wageningen University, Wageningen, NL (2013)

With references, with summaries in English and Dutch

ISBN: 978-94-6173-814-1

v

Table of Contents

Chapter 1 Mechanistic Driven Modeling and Optimization to Produce Dried

Healthy Food Products: State of Art and Challenges ............................................... 1

1.3 Influence of pre-treatments and drying conditions on quality retention ........ 4

1.4 Energy demand for drying .............................................................................. 5

1.5 Research challenges ....................................................................................... 6

1.6 Simultaneous optimization of product quality and energy efficiency ............ 9

1.7 Mechanistic driven modeling and optimization ........................................... 10

1.8 Non-destructive methods to quantify the moisture distribution ................... 12

1.9 Thesis structure ............................................................................................ 13

Chapter 2 Evaluation of the Free Volume Theory to Predict Moisture Transport

and Quality Changes during Broccoli Drying ........................................................ 21

2.1 Introduction .................................................................................................. 23

2.2 Theory and Modeling ................................................................................... 24

2.3 Results .......................................................................................................... 31

2.4 Conclusions .................................................................................................. 43

Chapter 3 Moisture Sorption Isotherms of Broccoli Interpreted with the Flory-

Huggins Free Volume Theory ................................................................................ 47

3.1 Introduction .................................................................................................. 49

3.2 Materials and Methods ................................................................................. 51


3.4 Results and Discussions ............................................................................... 59

3.5 Conclusions .................................................................................................. 68

Chapter 4 Anomalies in Moisture Transport during Broccoli Drying Monitored

by MRI? .................................................................................................................. 73

4.1 Introduction .................................................................................................. 75


4.3 Results and Discussions ............................................................................... 81

vi

4.4 Conclusions .................................................................................................. 89

Chapter 5 Quantifying Broccoli Drying Rates from MRI Measurements

................................................................................................................................ 93

5.1 Introduction .................................................................................................. 95



5.4 Results and Discussions ............................................................................. 103

5.5 Conclusions ................................................................................................ 111

Chapter 6 Drying Strategies to Retain Nutritional Components in Broccoli

.............................................................................................................................. 117

6.1 Introduction ................................................................................................ 119

6.2 Theory and Modeling ................................................................................. 120

6.3 Results and Discussions ............................................................................. 127

6.4 Conclusions ................................................................................................ 136

Chapter 7 Mechanistic driven modeling and optimization for drying of healthy

foods: Retrospectives and Perspectives ................................................................ 141

7.1 Energy efficient drying of healthy food products ...................................... 142

7.2 Mechanistic driven modeling and optimization for drying of healthy foods:

Retrospectives ................................................................................................... 143

7.3 Mechanistic driven modeling and optimization for drying of healthy foods:

Perspectives ....................................................................................................... 147

Summary............................................................................................................... 151

Samenvatting ........................................................................................................ 155

Acknowledgement ................................................................................................ 159

About the author ................................................................................................... 163

List of Publications ............................................................................................... 165

Overview of Completed Training Activities ........................................................ 167

Chapter 1

Mechanistic Driven Modeling and

Optimization to Produce Dried

Healthy Food Products: State of Art

and Challenges

Chapter 1

2

1.1 drying of vegetables

Food, either in natural or in processed form, provides energy and essential nutrients

for human life. A diet rich in essential nutrients has a positive effect on the human

condition. The essential nutrients for humans are carbohydrates, proteins, fats,

vitamins and minerals. Vitamins and anti-oxidants in fresh food strengthen the

immune system. For example, lycopene contributes to the reduction of prostate,

lung and breast cancers, and also a broad range of epithelial cancers (Shi et al.,

2000, Goula et al., 2006, Chang et al., 2007, Dewanto et al., 2002). Glucosinolates

have significant anticarcinogenic properties in the context of colorectal cancer

(Verkerk et al., 2004, Verkerk et al., 2009, Volden et al., 2009, Cieslik et al., 2007).

Fresh cultivated fruits and vegetables contain several essential nutrients, but due to

the high moisture content these fresh products have a short shelf life. One of the

most applied preservation methods to extend shelf life is drying. At low moisture

content the water activity is low and consequently the microbial activity. It allows

preservation of foods over a prolonged period. This technology can be traced back

to ancient times when people used sun and wind for natural drying of foods. The

experience of thousands of years and modern research resulted in various drying

methods and drying equipment. Among the available methods convective drying

with heated air is one of the most applied methods to preserve vegetable and fruit

products. The heat load of this method causes, however, quality changes (color,

flavor, texture and nutritional components) in food during drying.

In recent years the demand of consumers in the industrialized world for

convenience and processed food products expanded and at the same time also the

expectations on product quality, safety nutritional values and sustainability

increased. This drives the need for research on drying technologies that retain

quality attributes.

1.2 Broccoli

Brassica vegetables (cabbage, cauliflower, broccoli, Brussels sprouts etc.) are

common, not only because of the taste but also because of the nutritional

components having a positive effect on healthiness. It has been observed that a diet

rich in Brassica vegetables can reduce the risk of lung, stomach, colon cancers

State of art and challenges

3

(Murillo and Mehta, 2001, Verkerk et al., 2004, Volden et al., 2009). Although the

mechanism of the reduction of these cancers is not clear, the anti-oxidants in these

products (vitamin C, polyphenols, carotenoids, glucosinolates) play a role in the

reduction (Gliszczynska-Swiglo et al., 2011, Middleton and Kandaswami, 1993).

Two groups of enzymes in foods are involved in carcinogenic development; 1)

phase I enzymes which, depending on the conditions, can activate or deactivate

carcinogens, and 2) phase II enzymes that detoxify carcinogens. Inhibition of phase

I enzymes, and induction of phase II enzymes suppresses cancer development.

Brassica vegetables have a high content of glucosinolates which can be hydrolysed

by myrosinase to isothiocyanate, nitrile and thiocyanate (Figure 1) (Verkerk et al.,

2001). In in vivo studies it was observed that isothiocyanate can inhibit phase I

enzymes that activate carcinogens, and induces phase II detoxification of

carcinogens (Jones et al., 2006). Glucosinolates and myrosinase are present in

vacuoles and myrosin cells, respectively, and due to this separation the product

does not hydrolyze spontaneously. The hydrolysis occurs only when the cell walls

are broken down, for example by cutting, chewing or by heat treatments.

The moisture content of fresh broccoli ranges between 87-93% (wet basis). Due to

the high moisture content the shelf life of broccoli at low temperatures (3-4°C) is

limited to 7-10 days after harvest. To increase the shelf life drying can be applied

to reduce the water activity. Drying can also be used to produce broccoli

ingredients for convenience foods (soup powders, vegetable croutons, frozen food

products). An interesting option is to activate bioactivity during drying. However,

as bioactive components are heat sensitive, the drying system and the operational

conditions should be carefully chosen to retain bioactivity.

Chapter 1

4

Figure 1 Schematic diagram of hydrolysis of glucosinolates (Verkerk et al., 2001).

1.3 Influence of pre-treatments and drying conditions on quality retention

Besides the activation and retention of bioactive compounds other quality attributes

for dried products, like color, porosity, texture, flavor, have to be taken into

account. It is therefore important to notice that drying is not the only unit in the

chain of vegetable processing. It includes pre-treatment (washing, peeling,

blanching etc.), drying and post-treatment (packaging, storage etc.). These

treatments affect the quality attributes positively (digestibility, color bioavailability,

Krokida et al., 2000) and negatively (breakdown of enzymes and micronutrients,

Munyaka et al., 2010, Selman, 1994, Cieslik et al., 2007).

Prior to drying of vegetables, thermal pre-treatments may be needed. The enzymes

peroxidase and lipoxygenase in fresh vegetables cause enzymatic reactions that

result in color changes (turning products from green into brown) and unpleasant

odor (Vamos-Vigyzao, 1995, McEvily et al., 1992). Therefore, before drying,

vegetables are blanched to inactivate these enzymes which results in improved

color and taste. Furthermore, blanching breaks down the internal cell walls, softens

the internal tissue, and influences the elastic properties, which in turn enhance the

drying rate and yields uniform shrinkage behavior (Kunzek et al., 1999, Munyaka

et al., 2010, Waldron et al., 2003).

For water or steam blanching, the blanching temperatures range between 70-100 °C

and the time between 1-10 minutes. Soluble solids partly leach to the blanching


5

medium and compounds necessary for the formation of bioactive products may be

inactivated as well. For example, blanching procedures (both steaming and water

blanching) reduce the vitamin C content up to 40% of the initial value (Selman

1994, Vallejo et al. 2002). Mild blanching conditions are therefore required to

reduce vitamin C degradation. In a recent study Munyaka et al. (2010) showed that

high temperature-short time blanching retains vitamin C better than long time low

temperature blanching. Water blanching reduces glucosinolates content to 45-58%

of the initial content, while with steam blanching 80-82% of the initial value is

retained (Vallejo et al. 2002, Volden et al. 2009).

When blanching is a necessary step prior to drying, loss of nutritional components

cannot be avoided. The loss of the remaining components should be minimized

during drying. A significant advantage of blanching with respect to drying is the

softening of the internal tissue which results in an increased drying rate (Lewicki,

1998, Jin et al., 2012) and thus in a shorter drying time, less degradation of

components and less energy consumption.

Temperature is a major factor for quality degradation during drying. For convective

drying the air temperature in the dryer is often in the range of 40 to 70°C and the

product temperature varies between the wet bulb temperature and the air

temperature. For products with a long residence time in dryer the degradation of

components is significant. Vega-Galvez et al. (2009) reported that for convective

drying, vitamin C content falls below 40% of the initial value and that the retention

decreases with increasing temperature. Similar results were reported by Goula and

Adamopoulos (2006) and Zanoni et al (1998) for the degradation of Vitamin C

during drying, and by Oliviero et al. (2012, 2013) for the degradation of

glucosinolates and myrosinase during drying of broccoli. Therefore, mild drying

conditions and a short residence time in dryer are required to retain these bioactive

components.

1.4 Energy demand for drying

In convective drying, moisture vaporizes from the product. The heat required for

vaporization makes drying one of the most energy intensive processes. According

to a survey by Bahu (1991) in 1988, drying accounted at least 10% of the industrial

energy demand in the UK and Europe. As drying is limited by a thermodynamic

Chapter 1

6

barrier and because of the market introduction of new dried products (functional

foods, fast foods, and pharmaceuticals) the energy demand of drying has increased.

Despite governmental programs for energy reduction in industry, drying accounts

now for 15-20% of the total industrial energy consumption in developed countries

(Kemp, 2012). Furthermore, about 85% of all installed industrial dryers are

convective dryers with low energy efficiency (often below 50%) (Kudra, 2012).

The energy efficiency is defined as the ratio of energy for moisture evaporation and

the total energy supplied to the dryer. For convective drying, the energy efficiency

is based on the inlet air temperature (°C), the drier outlet air temperature

(°C) and the ambient temperature (°C):

(1)

The latent heat for vaporization varies with temperature and ranges between 2501

and 2256 kJ.kg-1

over the temperature range of 0 and 100°C. Therefore, to remove

1 kg of moisture from a product in a dryer operating with 50% energy efficiency,

over 4500 kJ.kg-1

energy is required. In addition, extra energy is required to heat

the product to the drying temperature and to compensate for heat losses from the

dryer. The state of art in the reduction of energy consumption is heat recovery,

adjusting the operation conditions or to reduce heat loss with insulation (Kemp,

2012). Retaining product quality requests for low temperature drying, this

according to equation 1 has low energy efficiency. The demands towards product

quality and energy efficiency appear to be two conflicting aims!

1.5 Research challenges

In convective driers for vegetables the product temperature varies between the wet

bulb temperature and the air temperature which is in the range of 40 to 70°C.

Investigations showed that for products that reside at these temperatures the

degradation of nutritional components is significant (Vega-Galvez et al., 2009,

Goula and Adamopoulos, 2006, Zanoni et al., 1998, Oliviero et al., 2012, 2013).

To retain these components during drying, mild drying at low temperatures should

be applied. However, the energy efficiency at low temperatures is low. Although

quality is regarded as the most important performance indicator, the energy


7

consumption needs increasing attention to reduce the operational costs and to

reduce the energy consumption and the emission of greenhouse gasses. Therefore

retention of heat sensitive components needs to be combined with energy

efficiency which brings two, possibly conflicting, challenges in drying research.

The demands of mild and sustainable drying bring the research challenge for

drying research.

How to dry vegetables with a high retention of nutritional components

and high energy efficiency?

This PhD research project on quality retention in combination with energy saving

(this thesis) is part of a larger research project ―Energy efficient drying of healthy

food products‖. The PhD projects in this context were:

1. Influence of drying technology on stability and availability of

glucosinolates in broccoli (Teresa Oliviero, thesis writing in progress),

2. Drying of healthy foods: from mechanism to optimization (this thesis), and

3. Energy-efficient low-temperature drying using adsorbents (J.C. Atuonwu,

PhD thesis Wageningen University, March 2013)

The goal of this thesis within the overall program is to investigate whether the

problem of apparently conflicting demands on quality retention and energy

efficiency can be solved by optimization. As the optimal drying strategy is

expected not to be solved straightforward, an accurate, mechanistic description of

the process and product degradation is required. The mechanistic description of the

product degradation is obtained from Project 1. The results from Project 3 can add

values to the improvement of energy efficiency.

Mishkin et al. (1984) were the pioneers in using optimization methods to improve

the quality of dried food products. Banga et al. (1991, 1994) used various objective

functions to optimize quality, energy efficiency or process time for drying.

However, these optimization problems considered only one objective at a time.

Kaminski et al. (1989), Madamba (1997), Kiranoudis & Markatos (2000) propose

to apply multi-objective functions to meet the different requirements in food

processing.

Maximizing product quality and energy efficiency are the key performance

indicators. Afzal et al. (1999) investigated the influence of temperature and air

Chapter 1

8

velocity on quality and energy consumption via experiments. Caceres-Huambo and

Menegalli (2009) maximized equipment loading and degradation of ascorbic acid

in fruits during drying via numerical modeling. However, the combination of

optimizing drying policy for energy efficiency and retention of multiple nutritional

values is still missing. This will be the focus of this thesis. Therefore, the first

research challenge for this thesis will be:

1. Can the optimization problem for mild, sustainable drying of

healthy vegetables be solved by use of mechanistic modeling?

To solve such an optimization problem, models for moisture transport and sorption

isotherm, kinetic models for bioactivity and models for energy efficiency are

required. Food is complex soft matter which contains water/moisture,

carbohydrates, fat, protein and ash. Drying of food and especially vegetables is

effected by the interaction between these components and phase changes in the

product matrix. Such physical and chemical changes effect progress of drying and

should be reflected in the used model. Most drying models in literature take the

coupled mass and heat transport phenomena into account (Mulet et al., 1999, Bon

et al., 1997), but not the physical changes in the product matrix and the interaction

between the components. The aim of this thesis work was to use a mechanistic

driven modeling and optimization approach to produce healthy food. The second

research question is:

2. How to describe the drying rate and moisture sorption isotherm by

models based on physical properties related to the product matrix?

Due to the temperature and moisture gradients in the drying products, the

degradation of nutritional components varies throughout particles that are being

dried. Models assume ideal transport of moisture in the product matrix. However,

validation of this assumption is still lacking. Therefore, the third research question

is:

3. How to validate moisture transport models and how to detect

moisture transport phenomena non-destructively, qualitative and

quantitatively?

In this overview of challenges, measurements and modeling of the degradation

kinetics of nutritional components is missing. This essential work is part of the


9

parallel thesis work of Mrs. T. Oliviero (Product Design and Quality Management

Group, Wageningen University). In this thesis, the kinetic results of her work are

used to minimize product quality loss.

To realize the solutions for the above mentioned research questions a mechanistic

drying modeling and optimization approach is used. The applied research scheme

and required information are introduced in the following sections.

1.6 Simultaneous optimization of product quality and energy efficiency

Two ways of optimization can be considered: static and dynamic optimization.

Static optimization searches for the best constant operational conditions or design

parameters, and does not use the transient properties of the process. Drying of

foods, however, include various stages of moisture transfer, for which dynamic

optimization is more suitable. Dynamic optimization results in optimal trajectories

for the operational conditions during the passage of food products through a dryer.

The optimization uses an objective function, can deal with constraints, and can be

applied to real production systems. The optimized trajectories can be continuous

functions (Bryson, 1999) or discrete functions (piece wise constant or piecewise

linear) (Banga et al., 2005). Discrete functions have the advantage that they can

represent succeeding drying stages. For example, Banga et al. (2003) and Chou &

Chua (2001) show that for drying of heat sensitive foodstuffs the use of multiple

drying chambers, each operating at its optimal level, could lead to better products

with significant energy savings.

The dynamic optimization requires knowledge of the drying system formulated as

a mathematical model and constraints. A drying model for product particles based

on mass and energy balances, physical properties and drying rates, and a quality

model for the degradation of nutritional components. All required elements are

given in Figure 2.

In this thesis we aim to use mechanistic models using physical and chemical

relations and that also consider the spatial distribution of moisture, temperature and

nutritional components. The drying model uses thermodynamic properties and

takes the mobility of water in the product into account (for example by the glass

transition temperature). Measurements of physical properties of broccoli are used

Chapter 1

10

in this thesis. In the product quality model myrosinase, glucosinolates and vitamin

C in broccoli and the degradation of these components as a function of heat load

and moisture levels are considered.

Drying model Quality model

Optimization

Quality & Energy Efficiency

Sorption

isotherm

Drying rate

Glucosinolates

Vitamins C

Drying in

MRI

Myrosinase

Constraints

Physical

properties

Pilot dryer

Pre-treatment

(blanching)

Pre-treatment

(blanching)

Experimental

Evaluation

Shrinkage

Healthy

quality

Energy

efficiency

Figure 2 Research scheme according to the objective of this thesis work. The optimization

uses a quality and a drying model. The quality model focusses on the retention of

myrosinase, glucosinolates and vitamin C. The drying model involves physical properties,

sorption isotherm and drying rates.

1.7 Mechanistic driven modeling and optimization

Figure 2 shows the combination of the kinetics on degradation of nutritional

components with the drying kinetics. The degradation of nutritional components is

a chemical process while drying is a multi-physics process. Models for the drying

kinetics and sorption isotherm should therefore be based on the physical properties

of the food matrix. As stated before food products as vegetables have a complex

matrix due to interaction between the involved components and their effect on the

mobility of water. For a good prediction of drying, which is a requirement for

optimization; models that reflect the mechanism of moisture transport throughout

the product matrix are required.

Optimization techniques have been well developed and have been applied in food

process optimization (Hadiyanto et al, 2007). The majority of the process models,


11

however, are still empirical or semi-empirical. Therefore, the emphasis of this

thesis is to use mechanistic drying models (Figure 3). The mechanistic models used

in this work are based on the Free Volume theories. To our knowledge, this is the

first time that these theories are used for moisture transport in a food matrix in

combination with quality models for nutritional components and used for the

optimization drying trajectories.

Mechanism based

model development

Mechanism based

sorption isotherm

model

Mechanism based

drying model

Model validation OptimizationExperimental

Evaluation

Flory Huggins Free

Volume theory

Free Volume

theory

Healthy quality

Energy efficiency

Figure 3 Physics driven modeling and optimization approach

1.7.1 Drying rates based on Free Volume theory

In drying of food products two periods can be distinguished; 1) the constant rate

period, and 2) the falling rate period. For vegetable drying the constant rate period

is very short; drying of broccoli is diffusion controlled (see for example Mulet et

al., 1999). Fick‘s second law is the basis for modeling the internal moisture

transport during diffusion controlled drying. It is commonly accepted that the

effective diffusion coefficient in Fick‘s law is temperature dependent according the

Arrhenius equation. This relation, however, has its limitations for food products.

During drying the state of the food matrix changes from rubbery to glassy, which

influences the mobility of water and hence the diffusion process. Mulet et al. (1999)

propose to extend the Arrhenius equation with moisture dependent terms. Slade

and Levine (1991) propose as an alternative to link the low moisture diffusion

coefficient in the low moisture content range with glass transition temperature.

However, their work is not supported by a quantitative model and calculations. In

this thesis we use for the falling rate period the Free Volume Theory, which

Chapter 1

12

involves moisture mobility and state changes during drying (Vrentas and Duda

1977, Vrentas and Vrentas, 1994, He et al., 2008, van der Sman and Meinders,

2013).

1.7.2 Sorption isotherm model based on Flory Huggins Free Volume theory

The moisture sorption isotherm relationship is also essential for the drying rate. It

presents the relationship between moisture content and water activity and provides

information on the equilibrium of the sorption of moisture in food at constant

temperatures. Besides being important for the boundary conditions during drying,

the moisture sorption isotherms also provide information on the storage conditions.

State of the art sorption isotherm relations are (semi)-empirical models (GAB, BET

etc.) which are based on theory for sorption at hard surfaces. Moisture sorption in

food matrices differs from moisture sorption on hard surfaces, and these

differences have to be taken into account. In this thesis the Flory-Huggins Free

Volume theory (Vrentas & Vrentas, 1991, Ubbink et al., 2007, Zhang and Zografi,

2001, van der Sman, 2013) has been applied to describe the sorption isotherms for

fresh and pre-treated foods.

1.8 Non-destructive methods to quantify the moisture distribution

Diffusion results in a moisture gradient with the highest moisture contents in the

center and the lowest at the edge of the product particles. Concentration driven

transport is a common assumption for drying of foods (Fick‘s law). One goal of

this thesis is to quantitatively validate the internal moisture transport and the spatial

distribution of moisture during drying. State of the art methods to measure the

internal distribution are destructive methods (e.g. by taking slices from the sample)

or non-destructive methods (e.g. γ ray densitometry). The disadvantage of these

methods is the limitation on the sample size, limited resolution and the

measurement in only one dimensional direction (McCarthy et al., 1991, Ruiz-

Cabrera et al., 2005, Chen, 2007). In this thesis MRI (Magnetic Resonance

Imaging) is applied as a non-destructive method to monitor and to understand the

actual drying behavior.


13

1.9 Thesis structure

The overall thesis structure is presented in Figure 5. There are three main parts in

this thesis: model development, model validation, model based dynamic

optimization and validation.

First of all, to meet the objective of this project, a drying model is developed. In

Chapter 2, the Free Volume Theory is presented as a model for drying. This model

is based on physical properties of food, and the mobility of moisture in the product

matrix during drying. With this theory, mass and heat transport, shrinkage, and

vitamin C degradation during drying are simulated by a spatial model. The sorption

isotherm is a key element in the drying model; it defines the relation between

moisture content and water activity and gives the boundary conditions for mass

transfer. In Chapter 3, the Flory-Huggins Free Volume theory is introduced to

interpret the sorption isotherm of broccoli. The main advantage of this theory is

that it takes into account the mixing properties of water, biopolymers and solutes.

Since it is based on product composition and physical properties, it has potential to

describe the sorption isotherm relation for large ranges of products, moisture

contents, and temperatures.

Drying model

Free Volume Theory

Optimization

Quality & Energy Efficiency

Sorption Isotherm model

Flory-Huggins Free Volume Theory

Model Validation

MRI Experiments

Drying Mechanism & Spatial Distribution

Drying rate derived from MRI

Experiments with pilot dryer

Model Development

Chapter 2 Chapter 3

Chapter 4 Chapter 5

Chapter 6

Figure 4 Thesis structure

Chapter 1

14

Chapter 4 and Chapter 5 concern the validation of the drying model based on the

Free Volume theories presented in Chapter 2 and Chapter 3. The validation of

moisture transport and distribution with a non-destructive technique, Magnetic

Resonance Imaging (MRI), to monitor moisture transport during drying is given in

Chapter 4. The results show the moisture distribution, drying rate, and shrinkage

of different pre-treated samples. Anomalous moisture transport is found which is

probably due to stress induced diffusion by the elastic impermeable skin.

In Chapter 5, drying rates of different pre-treated samples are derived from MRI

experimental data. Key parameters of Free Volume Theory based drying model are

tuned and the drying behavior of single particles in the MRI unit is compared with

the results from a pilot dryer

Chapter 6 concerns the dynamic optimization to find optimal drying trajectories

that increase both energy efficiency and product quality. The moisture-temperature

state diagram is used to interpret the calculated optimal trajectories. The results

presented in the state diagram shows that the optimal drying trajectories

circumvent the area with significant product quality degradation rates.

In the end, Chapter 7 gives the conclusion of this project, and the perspectives for

further development.


15

References

Bahu, R., (1991). Energy considerations in dryer design, 7 th International Drying

Symposium in conjunction with the CSISA'90 Congress, Prague, Czech, 08/90, pp. 553-

567.

Banga, J.R., Balsa-Canto, E., Moles, C.G., Alonso, A.A., (2003). Improving food

processing using modern optimization methods. Trends in Food Science & Technology

14(4), 131-144.

Banga, J.R., Balsa-Canto, E., Moles, C.G., Alonso, A.A., (2005). Dynamic optimization of

bioprocesses: Efficient and robust numerical strategies. Journal of Biotechnology

117(4), 407-419.

Banga, J.R., Paul Singh, R., (1994). Optimization of air drying of foods. Journal of Food

Engineering 23(2), 189-211.

Banga, J.R., Perez-Martin, R.I., Gallardo, J.M., Casares, J.J., (1991). Optimization of the

thermal processing of conduction-heated canned foods: Study of several objective

functions. Journal of Food Engineering 14(1), 25-51.

Bon, J., Simal, S., Rosselló, C., Mulet, A., (1997). Drying characteristics of hemispherical

solids. Journal of Food Engineering 34(2), 109-122.

Chang, C.H., Liu, Y.C., (2007). Study on Lycopene and Antioxidant Contents Variations in

Tomatoes under Air-Drying Process. Journal of Food Science 72(9), E532-E540.

Chen, X.D., (2007). Moisture Diffusivity in Food and Biological Materials. Drying

Technology 25(7-8), 1203-1213.

Chou, S.K., Chua, K.J., (2001). New hybrid drying technologies for heat sensitive

foodstuffs. Trends in Food Science & Technology 12(10), 359-369.

Cieślik, E., Leszczyńska, T., Filipiak-Florkiewicz, A., Sikora, E., Pisulewski, P.M., (2007).

Effects of some technological processes on glucosinolate contents in cruciferous

vegetables. Food Chemistry 105(3), 976-981.

Dewanto, V., Wu, X., Adom, K.K., Liu, R.H., (2002). Thermal Processing Enhances the

Nutritional Value of Tomatoes by Increasing Total Antioxidant Activity. Journal of

Agricultural and Food Chemistry 50(10), 3010-3014.

Gliszczyńska-Świgło, A., Ciska, E., Pawlak-Lemańska, K., Chmielewski, J., Borkowski, T.,

Tyrakowska, B., (2006). Changes in the content of health-promoting compounds and

Chapter 1

16

antioxidant activity of broccoli after domestic processing. Food Additives &

Contaminants 23(11), 1088-1098.

Goula, A.M., Adamopoulos, K.G., (2006). Retention of Ascorbic Acid during Drying of

Tomato Halves and Tomato Pulp. Drying Technology 24(1), 57-64.

Goula, A.M., Adamopoulos, K.G., Chatzitakis, P.C., Nikas, V.A., (2006). Prediction of

lycopene degradation during a drying process of tomato pulp. Journal of Food

Engineering 74(1), 37-46.

Hadiyanto, Asselman, A., Straten, G.v., Boom, R.M., Esveld, D.C., Boxtel, A.J.B.v.,

(2007). Quality prediction of bakery products in the initial phase of process design.

Innovative Food Science & Emerging Technologies 8(2), 285-298.

He, X., Fowler, A., Menze, M., Hand, S., Toner, M., (2008). Desiccation Kinetics and

Biothermodynamics of Glass Forming Trehalose Solutions in Thin Films. 36(8), 1428-

1439.

Jin, X., van Boxtel, A.J.B., Gerkema, E., Vergeldt, F.J., Van As, H., van Straten, G., Boom,

R.M., van der Sman, R.G.M., (2012). Anomalies in moisture transport during broccoli

drying monitored by MRI? Faraday Discussions 158(0), 65-75.

Jones, R.B., Faragher, J.D., Winkler, S., (2006). A review of the influence of postharvest

treatments on quality and glucosinolate content in broccoli (Brassica oleracea var.

italica) heads. Postharvest Biology and Technology 41(1), 1-8.

Kaminski, W., Zbicinski, I., Grabowski, S., Strumikko, C., (1989). MULTIOBJECTIVE

OPTIMIZATION OF DRYING PROCESS. Drying Technology 7(1), 1-16.

Kemp, I.C., (2012). Fundamentals of energy analysis of dryers. Wiley-VCH: Weinheim,

Germany.

Kiranoudis, C.T., Markatos, N.C., (2000). Pareto design of conveyor-belt dryers. Journal of

Food Engineering 46(3), 145-155.

Krokida, M.K., Kiranoudis, C.T., Maroulis, Z.B., Marinos-Kouris, D., (2000). EFFECT OF

PRETREATMENT ON COLOR OF DEHYDRATED PRODUCTS. Drying

Technology 18(6), 1239-1250.

Kudra, T., (2012). Energy Performance of Convective Dryers. Drying Technology 30(11-

12), 1190-1198.


17

Kunzek, H., Kabbert, R., Gloyna, D., (1999). Aspects of material science in food

processing: changes in plant cell walls of fruits and vegetables. 208(4), 233-250.

Lewicki, P.P., (1998). Effect of pre‐drying treatment, drying and rehydration on plant tissue

properties: A review. International Journal of Food Properties 1(1), 1-22.

Madamba, P.S., (1997). Optimization of the Drying Process: An Application to the Drying

of Garlic. Drying Technology 15(1), 117-136.

McCarthy, M.J., Perez, E., Ozilgen, M., (1991). Model for transient moisture profiles of a

drying apple slab using the data obtained with magnetic resonance imaging.

Biotechnology progress 7(6), 540-543.

McEvily, A.J., Iyengar, R., Otwell, W.S., (1992). Inhibition of enzymatic browning in

foods and beverages. Critical Reviews in Food Science and Nutrition 32(3), 253-273.

Middleton, E., Kandaswami, C., Theoharides, T.C., (2000). The Effects of Plant Flavonoids

on Mammalian Cells:Implications for Inflammation, Heart Disease, and Cancer.

Pharmacological Reviews 52(4), 673-751.

Mulet, A., Sanjuán, N., Bon, J., Simal, S., (1999). Drying model for highly porous

hemispherical bodies. 210(2), 80-83.

Munyaka, A.W., Oey, I., Van Loey, A., Hendrickx, M., (2010). Application of thermal

inactivation of enzymes during vitamin C analysis to study the influence of acidification,

crushing and blanching on vitamin C stability in Broccoli (Brassica oleracea L var.

italica). Food Chemistry 120(2), 591-598.

Murillo, G., Mehta, R.G., (2001). Cruciferous Vegetables and Cancer Prevention. Nutrition

and Cancer 41(1-2), 17-28.

Oliviero, T., Verkerk, R., Dekker, M., (2012). Effect of water content and temperature on

glucosinolate degradation kinetics in broccoli (Brassica oleracea var. italica). Food

Chemistry 132(4), 2037-2045.

Ruiz-Cabrera, M.A., Foucat, L., Bonny, J.M., Renou, J.P., Daudin, J.D., (2005).

Assessment of water diffusivity in gelatine gel from moisture profiles. I––Non-

destructive measurement of 1D moisture profiles during drying from 2D nuclear

magnetic resonance images. Journal of Food Engineering 68(2), 209-219.

Selman, J.D., (1994). Vitamin retention during blanching of vegetables. Food Chemistry

49(2), 137-147.

Chapter 1

18

Shi, J., Maguer, M.L., (2000). Lycopene in Tomatoes: Chemical and Physical Properties

Affected by Food Processing. Critical Reviews in Food Science and Nutrition 40(1), 1-

42.

Sila, D.N., Smout, C., Vu, S.T., Van Loey, A., Hendrickx, M., (2005). Influence of

Pretreatment Conditions on the Texture and Cell Wall Components of Carrots During

Thermal Processing. Journal of Food Science 70(2), E85-E91.

Slade, L., Levine, H., Reid, D.S., (1991). Beyond water activity: Recent advances based on

an alternative approach to the assessment of food quality and safety. Critical Reviews in

Food Science and Nutrition 30(2-3), 115-360.

Ubbink, J., Giardiello, M.-I., Limbach, H.-J., (2007). Sorption of Water by Bidisperse

Mixtures of Carbohydrates in Glassy and Rubbery States. Biomacromolecules 8(9),

2862-2873.

Vallejo, F., Tomás-Barberán, F., García-Viguera, C., (2002). Glucosinolates and vitamin C

content in edible parts of broccoli florets after domestic cooking. 215(4), 310-316.

Vámos-Vigyázó, L., (1995). Prevention of Enzymatic Browning in Fruits and Vegetables,

Enzymatic Browning and Its Prevention. American Chemical Society, pp. 49-62.

Van der Sman, R.G.M., (2013). Moisture sorption in mixtures of biopolymer,

Disaccharides and water. Food Hydrocolloids 32(1), 186-194.

Van Der Sman, R.G.M., Meinders, M.B.J., (2013). Moisture diffusivity in food materials.

Food Chemistry 138(2-3), 1265-1274.

Vega-Gálvez, A., Di Scala, K., Rodríguez, K., Lemus-Mondaca, R., Miranda, M., López, J.,

Perez-Won, M., (2009). Effect of air-drying temperature on physico-chemical properties,

antioxidant capacity, colour and total phenolic content of red pepper (Capsicum annuum,

L. var. Hungarian). Food Chemistry 117(4), 647-653.

Verkerk, R., Dekker, M., (2004). Glucosinolates and Myrosinase Activity in Red Cabbage

(Brassica oleracea L. Var. Capitata f. rubra DC.) after Various Microwave Treatments.

Journal of Agricultural and Food Chemistry 52(24), 7318-7323.

Verkerk, R., Dekker, M., Jongen, W.M.F., (2001). Post-harvest increase of indolyl

glucosinolates in response to chopping and storage of Brassica vegetables. Journal of

the Science of Food and Agriculture 81(9), 953-958.

Verkerk, R., Schreiner, M., Krumbein, A., Ciska, E., Holst, B., Rowland, I., De Schrijver,

R., Hansen, M., Gerhäuser, C., Mithen, R., Dekker, M., (2009). Glucosinolates in


19

Brassica vegetables: The influence of the food supply chain on intake, bioavailability

and human health. Molecular Nutrition & Food Research 53(S2), S219-S219.

Volden, J., Bengtsson, G.B., Wicklund, T., (2009). Glucosinolates, l-ascorbic acid, total

phenols, anthocyanins, antioxidant capacities and colour in cauliflower (Brassica

oleracea L. ssp. botrytis); effects of long-term freezer storage. Food Chemistry 112(4),

967-976.

Vrentas, J., Vrentas, C., (1994). Solvent self-diffusion in glassy polymer-solvent systems.

Macromolecules 27(20), 5570-5576.

Vrentas, J.S., Duda, J.L., (1977). Diffusion in polymer—solvent systems. I. Reexamination

of the free-volume theory. Journal of Polymer Science: Polymer Physics Edition 15(3),

403-416.

Vrentas, J.S., Vrentas, C.M., (1991). Sorption in glassy polymers. Macromolecules 24(9),

2404-2412.

Waldron, K.W., Parker, M.L., Smith, A.C., (2003). Plant Cell Walls and Food Quality.

Comprehensive Reviews in Food Science and Food Safety 2(4), 128-146.

Zanoni, B., Peri, C., Nani, R., Lavelli, V., (1998). Oxidative heat damage of tomato halves

as affected by drying. Food Research International 31(5), 395-401.

Zhang, J., Zografi, G., (2001). Water vapor absorption into amorphous sucrose-poly(vinyl

pyrrolidone) and trehalose–poly(vinyl pyrrolidone) mixtures. Journal of Pharmaceutical

Sciences 90(9), 1375-1385.

21

Chapter 2

Evaluation of the Free Volume Theory

to Predict Moisture Transport and

Quality Changes during Broccoli

Drying

Chapter 2

22

Abstract

Moisture diffusion in porous broccoli florets and stalks is modeled by using the

free volume and Maxwell-Eucken theories. These theories are based on the

mobility of water and concern the variation of the effective diffusion coefficient

for a wide range of temperature and moisture content during product drying. Mass

and heat transport, shrinkage and vitamin C degradation during drying of broccoli

are simulated by a spatial model. The effective diffusion coefficient varies strongly

with product moisture content and temperature. Vitamin C degradation is high at

moisture contents around 2 kg water per kg dry matter. Influences of the size of

broccoli on drying rate are evaluated for several types of broccoli florets and stalks.

Keywords: broccoli drying, moisture transport, spatial model, free

volume theory, quality changes

This chapter has been published as X. Jin, R. G. M. van der Sman, A. J. B. van Boxtel

(2011). Evaluation of the Free Volume Theory to Predict Moisture Transport and Quality

Changes during Broccoli Drying, Drying Technology, Vol.29, Iss. 16

Evaluation of the Free Volume Theory to Predict Moisture Transport and Quality Changes

23

2.1 Introduction

Since low product moisture content allows a safe storage of food products over a

long period, drying has gained an important position in the food industry. Water

removal is the main function of drying, but at the same time quality changes will

take place. For example, changes in shape, texture, color, and deterioration of

nutritional components occur during drying. As quality becomes a more and more

important aspect of dried products, preservation of such qualities and minimization

of deterioration are more essential.

Broccoli is a common vegetable for most families, not only because of the taste but

also because of the components with nutritional value and components that

contribute to health (e.g. vitamin C and glucosinolates). However, as these

components are temperature sensitive, they may deteriorate during drying. From

this point of view low and moderate temperatures are requested for drying.

Furthermore, the changes in quality depend on the local moisture content and

temperature in the product rather than the average moisture content. With dynamic

distributed models the quality and moisture content during the drying process can

be predicted. These models are also essential to optimize the product quality.

To predict and to optimize the quality it is necessary to know the concentration and

temperature profiles in the product as a function of time. In drying there are

normally two main drying periods: the constant rate period and the falling rate

period. Mulet and Sanjuan [1]

showed that drying of broccoli is a diffusion

controlled process; capillary transport of water was not detected in their work.

For diffusion controlled drying, Fick‘s second law is usually applied to describe

mass transport. The effective diffusion coefficient which is estimated from drying

data represents the overall mass transport of water in the material to be dried. The

most common approach to describe the temperature dependency of the effective

diffusion coefficient is the Arrhenius equation [1, 2]

. Since the Arrhenius equation is

an empirical equation, it is limited in its application for complex systems such as

foods. At temperatures above the product glass transition temperature, the state of

the product matrix changes, and as a result the diffusive behavior changes.

Especially at low moisture contents where the mobility of water is low, the

diffusion coefficient fits not well to the Arrhenius equation. To deal with this

problem, it is proposed to include the influence of the moisture content by adding

Chapter 2

24

another factor to the Arrhenius equation[1,3]

, Levine and Slade[4]

, Achanta and

Srinvas [5]

analyzed the reasons of possible low diffusion coefficient in the low

moisture content region, by referring to the glass transition. However, a model that

includes these aspects is not given.

As an alternative, the effective diffusion coefficient can be predicted from the free

volume theory, which is used for diffusion of polymer solutions[6,7]

. The main idea

of this theory is that the free volume between polymer chains (voids) is the limiting

factor for diffusion. Water molecules move between such voids with acquired

sufficient energy to overcome forces attracting them to neighboring molecules[8,9]

.

The free volume theory is based on physical and chemical properties of the product

and involves the glass and state transition parameters of the polymeric chains in

food. By calculating the diffusion coefficient according the free volume theory, the

drying rate can be predicted over a large temperature and moisture content range. A

recent example on the moisture migration of trehalose solution drying introduces

this theory for drying of bio-products[10]

.

In this work the free volume theory is applied to broccoli drying. The result is

compared with the common diffusion model which uses the Arrhenius equation.

Furthermore, the moisture distribution in the product is given for a spatially

distributed model and the effect on product quality is determined. As the size of the

samples influences the drying time, different types of broccoli florets and stalks

are defined and the influence of size on the drying time is evaluated.

2.2 Theory and Modeling

2.2.1 Basic balance equations and boundary conditions

The mass balance equation according to Fick‘s second law is:

(

) (1)

with W the moisture content (kg water per kg dry matter), Deff the effective diffusion

coefficient (m2.s

-1), r the distance from the centre (m) and t the time (s) .


25

This equation is applied for florets and stalks by using respectively spherical and

cylindrical coordinates [2,11]

. Figure 1 shows how the natural structure of broccoli is

translated into a form for spatial calculations of moisture and temperature.

Figure 1 Top: the natural structure of broccoli, Bottom: the applied model structure for

broccoli

Heat transport follows Fourier‘s law:

(2)

With T the temperature (K), λ the thermal conductivity (W.K-1

.m-1

), Cpp the specific

heat of the product (J.kg-1

.K-1

), and ρp the product density (kg.m-3

). Again spherical

and cylindrical coordinates are applied for broccoli florets and broccoli stalks

respectively.

For the surface where r=R, the boundary condition for equation (1) is given by:

( )

(3)

sta lk

F loret

F

R

Chapter 2

26

with kc the mass transfer coefficient (m.s-1

), Csurface the vapor concentration at the

product surface (kg.m-3

) and Cair the vapor concentration in the air (kg.m-3

). This

equation indicates that the liquid flux to the surface equals to the vapor flux from

the surface to the bulk drying air.

Similarly, the boundary conditions for the heat balance equation (2) at the surface

with r=R is:

( )

(4)

with h as the heat transfer coefficient (W.m-2

.K-1

), ΔHevap the latent heat for

evaporation (J.kg-1

). The term

represents the amount of

energy required to evaporate the liquid flux at the product surface.

For the center of the product (r=0), there is no mass and heat transfer over that

surface of the drying product. Thus:

and

(5)

2.2.2 Effective diffusion coefficient based on Arrhenius theory

The Arrhenius equation is often used for the temperature dependency of the

effective diffusion coefficient Deff :

(6)

Simal and Rosselló [11]

propose the extension of the Arrhenius equation for the

cylindrical part of broccoli (stalks) by an extra term:

(7)

For the hemispherical part of broccoli (florets), Bon and Simal [2]

and Simal and

Rosselló[11]

give:


27

(8)

With W the moisture content (kg water per kg dry matter), R the gas constant

(8.314J.K-1

.mol-1

) and T (K) the temperature. The Arrhenius equation is an

empirical equation with its limitations in food products. Although it expresses the

temperature dependency, above the glass transition temperature the state of the

product matrix changes, resulting in changed diffusion properties. However, the

Arrhenius equation is not able to predict the diffusion in porous media like the

floret.

2.2.3 Effective diffusion coefficient based on Free Volume theory and Maxwell-

Eucken theory

In porous media the effective diffusion coefficient depends on the diffusion

properties of the dispersed phase (air) and continuous phase (product)[12]

. By using

the Maxwell-Eucken relationship, the diffusion coefficient for water in products is

composed from the diffusion coefficient of water in the continuous phase (Dc) and

in the dispersed phase (Dd):

(

) (9)

For moisture diffusion during broccoli drying, Dd is the water vapor diffusion

coefficient in the air and Dc is the mutual diffusion coefficient of water molecules

in food polymer chains. (-) is the porosity, which is low for the stalk and high for

the porous floret. The water vapor diffusion coefficient in the air is given by Olek

and Perre[13]

:

(

)

(10)

With P is the pressure (Pa), and T the temperature (K)

The mutual diffusion coefficient of water molecules in a food polymer matrix is a

combination of the self-diffusivity of the water molecules (Dw) and the self-

diffusivity of the solids (Ds). The mutual diffusivity for binary systems is given by

the Darken relation[14]

:

Chapter 2

28

(11)

(12)

with (-) is the volume fraction of the solid phase, Q (-) is a thermodynamic factor,

and χ (-) is the interaction parameter.

The self-diffusion coefficient of water (Dw) follows the free volume theory, which

considers physical properties of the product, such as water molecule mobility and

the glass transition temperature. The free volume theory predicts the effective

diffusion coefficient for a whole range of moisture contents and temperatures.

Vrents and Duda[6]

showed the application for polymer diffusion system, while He

and Fowler[10]

used this theory for moisture transport in sugars.

The water self-diffusivity in a polymer matrix is given by:

̂ ̂

(

)( )

(13)

with ΔE the activation energy (J.mol-1

), D0 the pre-exponential factor (m2.s

-1), ς the

ratio between molar volume of solvent versus solute (-), Kij the free volume

parameters (K), Tg,i the glass transition temperature of component i (K), yi the

mass fraction (%), and *

iV

the critical volume of component i (ml.g-1

).

Free volume parameters of water are given by He and Fowler [10] (See Table 1).

Sugars are the main building blocks in broccoli. The physical properties of sugars

are close and therefore we choose the free volume parameters of sucrose as

representative for the solids. These parameters are summarized in Table 2.


29

Table 1 Free volume parameters of pure water

Symbol Value

*

1V

(ml.g-1

) 0.91

Tg,1 (K) 136

D0 (m2.s

-1) 1.39×10

-7

ΔE (J.mol-1

) 1.98×103

K21 (K) -19.73

K11/γ (m.L.g-1

.K-1

) 1.945×10-3

Table 2 Free volume parameters of solid matrix of broccoli

Symbol Value

*

2V

(ml.g-1

) 0.59

Tg,2 (K) 360

K22 (K) 69.21

C1 11.01

C2 69.21

k (J.K-1

)

1.38×10-23

a (m) 1×10-9

Chapter 2

30

The remaining parameters are given by Vrentas and Vrentas[15]

:

(14)

̂

(15)

where C1 and C2 are universal constants.

The self-diffusivity of the solids (Ds) follows from the Stokes-Einstein theory [16]

:

(16)

With a the radius of the solid particle (m), ηeff the viscosity (Pa.s) and k the

Boltzmann constant.

The sorption isotherm relationship is used in the boundary condition for mass

transfer (equation 3). According to Mulet and Sanjuan[1]

the sorption isotherm for

broccoli is:

(17)

Mulet and Sanjuan[1]

observed also shrinkage during drying. Simal and Rosselló [11]

suggested a shrinkage model which is based on a proportional change of the

volume with the changes in moisture content:

(18)

According to their results, shrinkage only happens in radial direction.

2.2.4 Degradation of healthy components

As an indicator for components that contribute to health, vitamin C is considered.

Despite of the different sample nature, experiments on potato and pineapple

samples showed similar results for the vitamin C degradation rate constants[17,18]

.

These results are therefore also applied for broccoli. The degradation of vitamin C

follows a first order degradation kinetics:


31

(19)

with C the concentration (kg/m3) and k the rate constant (s

-1). The temperature

dependency of k is given as:

(20)

Mikshkin and Saguy[17]

and Karim and Adebowale[18]

found the following

expressions for the rate constant and activation energy of vitamin C degradation

during drying:

(21)

(22)

With P1-P7 as constants and W the moisture content (see Table 3)

Table 3 Vitamin C degradation kinetic model parameter values for Eq. (21) and (22)

Parameter Value Parameter Value

P1 16.38 P4 14831.0

P2 1.782 P5 241.1

P3 1.890 P6 656.2

P7 236.8

2.3 Results

2.3.1 Diffusion model for broccoli stalks

The free volume theory model was used to compute the effective diffusion

coefficient during diffusion controlled drying of broccoli stalks. It is assumed that

Chapter 2

32

capillary water transport is neglectable to the diffusive transport. Simulations were

done for cylindrical stalks of length 0.02m and radius 0.004m. he drying conditions

and the sample sizes were the same as in the work of Simal and Rosselló [11]

. They

reported effective diffusion coefficient values at 90°C between 1.63×10-9

to

2.25×10-9

(m2.s

-1) for different drying times (720s-2160s) and positions in the

product by using the Arrhenius equation. The diffusion coefficient values based on

the free volume theory range for these conditions from 1.56×10—9

to 3.20×10-9

(m2.s

-1).

Further simulations with the free volume theory were done for the effective

diffusion coefficient during drying of broccoli stalks. As the self-diffusion

coefficient of water molecules is influenced by the moisture content, a full range of

moisture contents was used. In Figure 2 (top) the effective diffusion coefficient is

expressed as a function of moisture content during drying and different product

temperatures. The figure shows that the obtained diffusion coefficients vary with

temperature and moisture content and are comparable to the results of Simal and

Rosselló [11]

. Especially at moisture contents, below 0.5 kg water per kg dry matter,

the results deviate from the literature values. Here, the free volume theory predicts

a lower diffusion coefficient because of the lower mobility of the water molecules.

For the diffusion coefficient a maximum value is found for a moisture content of 2

kg water per kg dry matter. Furthermore, the graph shows that, just like the

Arrhenius equation, the diffusion coefficient increases with raising temperature.

2.3.2 Diffusion model for broccoli florets

Similarly, the effective diffusion coefficient of drying of broccoli florets was

calculated. In the simulations, a diameter of 0.04m and an average porosity 0.2 was

used for the florets. Mulet and Sanjuan[1]

gave effective diffusion coefficients

based on the Arrhenius theory for the temperature range 35-70°C. Their reported

values of the effective diffusion coefficient were in the range of 3.00×10—8

to

6.23×10—8

(m2.s

-1). The values of the effective diffusion coefficient according the

free volume theory are lower and ranged from 0.86×10—8

to 1.67×10—8

(m2.s

-1)

over the temperatures range between 35-70°C.

Furthermore, the same simulations which have been done for broccoli stalks were

also done for broccoli florets for a wide range of moisture contents and


33

temperatures. The results are shown in Figure 2 (bottom). Again, the results are

comparable with literature values [1]

, except for the low moisture content range

where due to the lower water mobility the diffusion coefficient is low. Compared to

the broccoli stalks, the simulations show for the broccoli florets a ten times higher

value. This is result of the porous structure of the floret in which the air pockets

enhance diffusion.

Figure 2 Simulation results of effective diffusion coefficient of water in broccoli at

different temperatures. Top: broccoli stalk. Bottom: broccoli floret.

0 2 4 6 8 100

0.5

1

1.5

2x 10

-9

Moisture content (kg water / kg dry matter)

Def

f-st

alk (

m2s-

1)

20 °C

30 °C

40 °C

50 °C

0 2 4 6 8 100

0.5

1

1.5

2

2.5x 10

-8

Moisture content (kg water / kg dry matter )

Def

f-fl

ore

t (m

2s-

1)

20 °C

30 °C

40 °C

50 °C

Chapter 2

34

2.3.3 Drying simulation results

Dynamic drying simulations have been done in Comsol Multiphysics. A symmetric

2-D model was chosen according to the structure shown in Figure 1. The size of the

simulation sample was 0.02m in radius for the broccoli floret, 0.01m in radius and

0.02m in height for the broccoli stalk. To ensure diffusion controlled drying, the air

flow rate was set to 2.5 m.s-1

. Shrinkage of the sample was included as well (see

equation 18). The initial moisture content was set to 9.6 kg water per kg dry matter

and was uniform distributed throughout the whole sample. The initial temperature

of the product was 20°C.

Figure 3 shows the moisture distribution in broccoli after ten hours of drying. The

color surface gives the moisture distribution within broccoli. The temperature

distribution was also calculated, but after ten minutes drying, the temperature

profile was already equally distributed.

The figure shows that the moisture diffuses from the center to the outer surface in

the direction of the arrows. At the surface, moisture evaporates due to the mass

and energy exchange with the air and the surface dries first. Moisture content

increases towards the center of the product. The product gradually shrinks during

the drying process, and shrinkage is shown by comparing the current frame with

the original frame.

Compared to the stalk, the moisture profile for the floret is more uniform. This is a

result of the porous structure of the floret, which takes advantage of the diffusion

properties of water in air. However, as the dimensions of the floret are larger than

that of the stalk, drying of the floret takes more time.


35

Figure 3 Spatial moisture distribution in broccoli at 10 hours of drying at 50°C. Drying

starts at the outer frame which changes due to shrinkage to the colored frame. Coordinates

in meters.

Simulation results for different positions in stalk and floret are given in Figure 4.

The results concern different positions along the vertical axis (height) in the floret

and stalk. Each curve in Figure 4 indicates the local moisture variation as a

function of the drying time. The drying curves for the broccoli stalks differ for the

positions, the outer surface dries faster than the center core, whereas, the drying

curves for broccoli florets are close for the different positions.

Chapter 2

36

Figure 4 Top: Drying curves of broccoli stalk at different positions from top to bottom

along the vertical axis in the stalk (m). Bottom: Drying curves of broccoli floret at different

positions from bottom to top along the vertical axis in the floret (m)

2.3.4 Comparison the results from Free Volume theory and Arrhenius theory

Figure 5 shows the comparison between using the free volume theory and the

Arrhenius equation for the effective diffusion coefficient. The drying curve for the


37

average moisture content of the same piece of broccoli as considered in previous

section. The graph shows that after one hour drying the curves starts to deviate. As

the effective diffusion coefficient from the free volume theory is above that based

on the Arrhenius equation (see Figure 2), drying is faster. During drying the

differences in average moisture content increase. At low moisture contents, where

the mobility of water decreases, the diffusion coefficient from the free volume

theory falls below that of the Arrhenius equation. As a result, the drying curves

approach and cross each other. As the degradation rate of healthy components is

strongly coupled to the local moisture content, accurate moisture content prediction

is important.

Figure 5 Comparison of average moisture content based on Free Volume Theory and

Arrhenius theory

0 5 10 15 20 250

2

4

6

8

10

Time (hour)

Mois

ture

conte

nt

(kg w

ater

/ k

gdry

mat

ter)

Arrhenius Theory

Free Volume Theory

Chapter 2

38

2.3.5 Degradation of healthy components

Figure 6 gives the degradation rate constant for vitamin C degradation for a range

of moisture contents and temperatures. The degradation rate constant is a bell

shaped curve; above 4 kg water per kg dry matter the degradation rate is constant

and very low and there is a maximum value at moisture content of 2 kg water per

kg dry matter. The rate constants increase with increasing temperature.

Figure 6 Vitamin C degradation rate constant as a function of moisture content and

temperature.

The vitamin C concentration profiles resulting from drying are given in Figure 7.

The top figure, for t=10 hour, shows that at this moment degradation starts at the

bottom of the broccoli stalk. The floret and the major part of the stalk still have the

initial concentration. Till this moment, the moisture content in the major part of the

broccoli was above 4 kg water per kg dry matter, where vitamin C degradation

hardly occurs. Figure 7 shows also the concentration profiles at 15 hour and 16

hour drying. In this period, the moisture content of the whole body reach values

where the degradation rate constant increases rapidly. As a result of these

0 1 2 3 40

0.005

0.01

0.015

0.02

0.025

0.03

0.035

Moisture content (kg water / kg dry matter)

Rat

e co

nst

ant

k (

s-1)

50 °C

40 °C

30 °C

20 °C


39

conditions, the vitamin C concentration decreases fast. At 15 hours, vitamin C

concentration in the stalk is already low and the concentration starts to decrease in

the floret. At 16 hours, there is hardly any Vitamin C left.

Figure 7 Vitamin C distributions throughout the sample. Top: after 10 hour drying, middle:

after 15 hour drying, bottom: after 16 hour drying. Coordinates are given in meters

Chapter 2

40

2.3.6 Analysis of drying behavior of different sizes of broccoli

In the previous simulations, a piece of fresh broccoli (as shown in Figure 1) is

considered for drying. Due to the mild drying conditions and the large size of the

sample, drying takes a long time. In order to reduce the energy requirement and to

limit the size of drying equipment, the drying time should be lowered. Furthermore,

to limit the degradation the nutritious components like vitamin C, the time with

high values for the degradation rate constant (k; see Figure 6) should be as short as

possible.

Instead of a full piece of broccoli, separate parts can be dried. Due to the branch

structure of broccoli, the piece of broccoli from Figure 1 can be split up in smaller

florets and remaining cylindrical pieces of stalk. Simulations are done for three

sizes of florets, and four sizes of cylinders which are taken from the broccoli

structure in Figure 8. The sizes are specified in Table 4.

Figure 8 Cross section of a broccoli floret. Numbers refer to the different pieces to be dried.


41

Table 4 Size specification for the different types of broccoli florets (hemispherical and

cylindrical part) and stalks (cylindrical part only). Unit: m

Florets Diameter

(semispherical)

Height

(semispherical)

Diameter

(cylindrical)

Height

(cylindrical)

Type 1 0.04 0.02 0.02 0.02

Type 2 0.02 0.01 0.006 0.005

Type 3 0.005 0.005 0.002 0.002

Stalks Diameter

(cylindrical)

Height

(cylindrical)

Type 1 0.02 0.02

Type 2 0.004 0.005

Type 3 0.002 0.004

Type 4 0.001 0.004

The upper graph in Figure 9 shows the average moisture contents for the three

types of broccoli florets. Drying of a small sample is much faster than that of the

larger pieces. The smallest floret can be dried in a few hours, whereas the largest

one will need at least 24 hours to be dried.

Simulations for the different cylinders are given in the lower graph of Figure 9.

The difference in drying rates follows from the slopes of the curves and the time

required to reach the final moisture content. Compared to the initially given

structure, drying is much faster by splitting the sample into multi-cylinders and the

Chapter 2

42

smallest cylinder can be dried within one hour which could be an acceptable

residence time in industrial dryers.

Figure 9 Average moisture content in different sizes of broccoli florets (top) and stalks

(bottom) after 24 hour drying

0 5 10 15 20 250

1

2

3

4

5

6

7

8

9

10

Time (hour)

Mois

ture

conte

nt

(kg w

ater

/ k

g d

ry m

atte

r)

floret type1

floret type2

floret type3

0 5 10 15 20 250

1

2

3

4

5

6

7

8

9

10

Time (hour)

Mois

ture

conte

nt

(kg w

ater

/ k

g d

ry m

atte

r)

stalk type 1

stalk type 2

stalk type 3

stalk type 4


43

2.4 Conclusions

In this paper, the free volume theory combined with the Maxwell-Eucken theory is

used to predict the effective diffusion coefficient during drying of broccoli. The

obtained values from the proposed model are close to the effective diffusion

coefficient as given in the literature. Main advantage of the free volume theory is

that the mobility of water molecules is taken into account and that the glass

transition temperature is involved. As a consequence this model has the potential

to predict the effective diffusion coefficient from general physical and chemical

properties for a wide range of moisture contents and temperatures. The other

advantage is that by combining the free volume theory with the Maxwell-Eucken

theory, the moisture transport in the porous structure of a broccoli floret can be

predicted as well.

The effective diffusion coefficient from the free volume theory varies with the

product moisture content and temperature. As a consequence the drying curve

deviates from models where the effective diffusion coefficient is only a function of

temperature according to the Arrhenius equation.

By using a spatial model, temperature and moisture distribution, as well as

shrinkage is presented by the 2-D color map and a moving mesh function. The

temperature distribution in broccoli proved to be uniform after a relatively short

time. During drying at 50°C the moisture distribution in the broccoli floret is

homogeneous. The simulations show that a long drying time is required to bring

the broccoli moisture content to a level of 0.2 kg water per kg dry matter which is

the level for longer shelf life. However, by redefining the structures for drying,

drying time can be enhanced significantly. The spatial calculations make it possible

to estimate the content of healthy components (e.g. vitamin C) throughout the

product and as a function of time. At high moisture contents (>4kg water per kg

dry matter) the rate constant is very low and degradation hardly occurs. However,

the degradation rate is high at a moisture content of 2 kg water per kg dry matter.

So optimization towards optimal drying paths to limit degradation is required.

Chapter 2

44

References

1. Mulet, A., Sanjuan, N.and Bon, J., 1999. Drying model for highly porous

hemispherical bodies. European Food Research and Technology, 210:80-83.

2. Bon, J., Simal, S., Rosselló, C. and Mulet, A., 1997. Drying characteristics of

hemispherical solids. Journal of Food Engineering, 34(2): 109-122.

3. Chen, X.D., and Peng, X.F., 2005. Modified biot number in the context of air

drying of small moist porous objects. Drying Technology, 23:1, 83-103

4. Levine,H. and Slade, L.1991. In water relationships in foods: advances in 1980s

and trends for the 1990s. Plenum Press, New Yorl.

5. Achanta, Srinvas and Okos, Martin R. 1996. Predicting the quality of drhydrated

foods and biopolymers-research needs and opportunities. Drying Technology,

14:6,1329-1368.

6. Vrentas, J.S. and Duda, J.L., 1977. Diffusion in polymer - solvent systems. I.

Reexamination of the free-volume theory. Journal of Polymer Science: Polymer

Physics Edition, 15(3): 403-416.

7. Vrentas, J.S. and Vrentas, C.M., 1994. Evaluation of a sorption equation for

polymer-solvent systems. Journal of Applied Polymer Science, 51(10): 1791-1795.

8. Hong, S.-U., 1996. Predicting ability of free-volume theory for solvent self-

diffusion coefficients in rubbers. Journal of Applied Polymer Science, 61(5): 833-

841.

9. Nasrabad, A.E., Laghaei, R. and Eu, B.C., 2005. Modified free volume theory of

self-diffusion and molecular theory of shear viscosity of liquid carbon dioxide.

The Journal of Physical Chemistry B, 109(16): 8171-8179.

10. He, X.M., Fowler, A., and Menze, M., 2008. Desiccation kinetics and

biothermodynamics of glass forming trehalose solutions in thin films. Annals of

Biomedical Engineering, 36(8): 1428-1439.

11. Simal, S., Rosselló, C., Berna, A. and Mulet, A., 1998. Drying of shrinking

cylinder-shaped bodies. Journal of Food Engineering, 37(4): 423-435.

12. Bertoly, N., Chaves, A. and Zaritzky, N.E., 1990. Diffusion of carbon dioxide in

tomato fruits during cold storage in modified atmosphere. International Journal of

Food Science and Technology, 25(3): 318-327.

13. Olek, W.A., Perre, P. and Weres, J., 2005. Inverse analysis of the transient bound

water diffusion in wood. Holzforschung, 59(1): 38-45.

14. Hahn, H., Averback, R.S. and Rothman, S.J., 1986. Diffusivities of Ni, Zr, Au, and

Cu in amorphous Ni-Zr alloys. Physical Review B, 33(12): 8825.

15. Vrentas, J.S. and Vrentas, C.M., 1998. Predictive methods for self-diffusion and

mutual diffusion coefficients in polymer-solvent systems. European Polymer

Journal, 34(5-6): 797-803.

16. Crank, J., Park, G.S., Diffusion in Polymers, London: Academic Press, 1968


45

17. Mishkin, M., Saguy, I. and Karel, M., 1984. Optimization of nutrient retention

during processing: ascorbic acid in potato dehydration. Journal of Food Science,

49(5): 1262-1266.

18. Karim, O.R. and Adebowale, A.A., 2009. A dynamic method for kinetic model of

ascorbic acid degradation during air dehydration of pretreated pineapple slices.

International Food Research Journal, 16: 555-560

Chapter 2

46

47

Chapter 3

Moisture Sorption Isotherms of

Broccoli Interpreted with the Flory-

Huggins Free Volume Theory

Chapter 3

48

Abstract

In this work, the Flory Huggins Free Volume theory is used to interpret the

sorption isotherms of broccoli from its composition and using physical properties

of the components. This theory considers the mixing properties of water,

biopolymers and solutes and has the potential to describe the sorption isotherms for

varying product moisture content, composition and temperature. The required

physical properties of the pure components in food became available in recent

years and allow now the prediction of the sorption isotherms with this theory.

Sorption isotherm experiments have been performed for broccoli florets and stalks,

at two temperatures. Experimental data shows that the Flory Huggins Free Volume

(FHFV) theory represents the sorption isotherm of fresh and blanched broccoli

samples accurately. The results also show that blanching affects the sorption

isotherm due to the change of composition via leaching solutes and the change of

interaction parameter due to protein denaturation.

Keywords: sorption isotherm, Flory Huggins Free Volume theory, glass

transition, interaction parameter

This chapter has been published as X. Jin, R. G. M. van der Sman, J.F.C. van Maanen, H.C.

van Deventer, G. van Straten, R.M. Boom, A. J. B. van Boxtel (2013). Moisture Sorption

Isotherms of Broccoli Interpreted with the Flory-Huggins Free Volume Theory. Food

Biophysics, 1-9.

Moisture Sorption Isotherms Interpreted with the Flory-Huggins Free Volume Theory

49

3.1 Introduction

Water is the main component in fresh food products. One of the most common

ways for preservation of these products is removal of water by drying, such that the

water activity is sufficiently low (typically below 0.3). During drying, mass

transfer in the product is driven by (water) activity gradients. Moisture sorption

isotherms define the relation between concentrations and activities, and give the

boundary conditions for mass transfer. The measurement and estimation of

moisture sorption isotherms of products is therefore an essential aspect for

designing or modeling drying processes. Moreover, the moisture sorption

properties are important for the sensory, physical, chemical and biological

properties of dried products [1, 2].

Several (semi)-empirical expressions are known to adequately describe the

moisture sorption isotherm; for example Henderson, Oswin, Halsey, Chung-Pfost

equations, and the GAB equation, which has been adopted by the American

Society of Agricultural engineers as a standard for describing moisture sorption

isotherms [3-5]. The GAB equation is commonly used; its accuracy is high

compared to other relations [6-11]. Furthermore, the GAB equation is

recommended by the European project COST 90 on Physical Properties of Foods

[12].

These relations are, however, from a physical point of view not appropriate for

food materials. The GAB equation is an extension of the BET model, which

describes (inert) gas adsorption on hard surfaces. In food, water is not absorbed on

surfaces, but through molecular absorption inside the matrix. Thus, the

phenomenon is more related to mixing of solvent (water), (bio) polymer, and other

soluble solutes [13], which are commonly described by the Flory-Huggins theory.

The FHFV theory extends the FH (Flory Huggins) theory by taking into account

the structural (non

xin jin - wur...iii drying of healthy foods from mechanism to optimization xin jin thesis submitted...

Documents